Theorem:
The set of students who can learn the material of a course without attending lectures or working homework problems is always smaller than the set of students who think they can learn the material of a course without attending lectures or doing homework problems.
Years of intense study have so far failed to produce a counterexample to this theorem, but no airtight formal proof has yet been devised, either. The closest attempt attempts to prove it by assuming the opposite, and finding a contradiction, arguing that were the set of students who think they can learn without homework of equal or lesser size than the set of students who can learn without homework, there would be no need to collect and grade homework. And yet, faculty do collect and grade homework, which is drudgery. It would be irrational to collect and grade homework if it served no purpose, and as faculty are rational beings, we have arrived at a contradiction, and proved the theorem.
This attempted proof rests heavily on the controversial Axiom of Rationality, and thus is not generally accepted as valid. And so, the search for a proof of the No-Homework Theorem continues.
(I should note that this is not inspired by anything to do with my current class. Rather, it’s a reaction to some of the comments in this discussion thread, which was brought to my attention by somebody on FriendFeed.)